A317517 - OEIS

%I #4 Jul 30 2018 11:31:10

%S 1,2,2,4,8,4,8,32,32,8,16,128,255,128,16,32,512,2032,2032,512,32,64,

%T 2048,16193,32256,16193,2048,64,128,8192,129042,512096,512096,129042,

%U 8192,128,256,32768,1028335,8130048,16198017,8130048,1028335,32768,256,512,131072

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ...1......2........4...........8.............16...............32

%C ...2......8.......32.........128............512.............2048

%C ...4.....32......255........2032..........16193...........129042

%C ...8....128.....2032.......32256.........512096..........8130048

%C ..16....512....16193......512096.......16198017........512358002

%C ..32...2048...129042.....8130048......512358002......32289056648

%C ..64...8192..1028335...129072576....16206294085....2034862700902

%C .128..32768..8194796..2049155072...512618027974..128237436273216

%C .256.131072.65304285.32532368768.16214518668763.8081548422775938

%H R. H. Hardin, <a href="/A317517/b317517.txt">Table of n, a(n) for n = 1..420</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1)

%F k=2: a(n) = 4*a(n-1)

%F k=3: a(n) = 8*a(n-1) -a(n-2) +6*a(n-3)

%F k=4: a(n) = 16*a(n-1) -6*a(n-2) +64*a(n-3)

%F k=5: [order 8]

%F k=6: [order 15]

%F k=7: [order 34]

%e Some solutions for n=5 k=4

%e ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0

%e ..0..0..0..0. .0..1..0..0. .1..0..0..1. .1..0..1..1. .0..1..0..0

%e ..1..0..1..1. .1..1..1..1. .0..1..0..0. .1..1..1..0. .1..0..0..0

%e ..0..0..0..0. .1..0..0..1. .0..0..1..1. .1..0..0..1. .1..0..1..1

%e ..1..1..1..1. .1..1..1..0. .1..0..0..1. .0..0..1..0. .0..0..0..0

%Y Column 1 is A000079(n-1).

%Y Column 2 is A004171(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 30 2018